Mechanics of field-consistency in finite element analysis—a penalty function approach

Abstract

Although C° continuous beam, plate and shell elements have become very popular, a simple understanding of several difficulties such as shear locking, parasitic shear, stress oscillations, etc. is not yet available in the literature. In displacement type finite element formulations, these difficulties can be easily rationalized using “field-consistency” concepts and a priori quantitative error estimates of these difficulties can also be made using an operational procedure called the “functional re-constitution” technique. In this paper we demonstrate the mechanics of these concepts using the simplest shear flexible beam element (linear Timoshenko beam element) as an example, and verify its a priori projections through digital computations. The rationale behind the use of optimal stress sampling at Gaussian points is also derived directly from these arguments.